import json, numpy as np
d=json.load(open('die.json')); V=np.array(d['vertices']); G=np.array(d['G']); Nn=np.array(d['normals'],float)
faces=d['faces']; L=np.ptp(V[:,0])
nn=Nn/np.linalg.norm(Nn,axis=1)[:,None]
def edges_of(fi):
    f=faces[fi]; return [(f[a],f[(a+1)%len(f)]) for a in range(len(f))]
def adj(fi,e):
    s=set(e)
    for g in range(14):
        if g!=fi and s<=set(faces[g]): return g
def info(fi,Gp=G):
    n=nn[fi]; f=V[faces[fi]]; P=Gp+np.dot(f[0]-Gp,n)*n
    out=[]
    for (a,b) in edges_of(fi):
        A,B=V[a],V[b]; e=B-A
        s=np.dot(np.cross(e,P-A),n)/np.linalg.norm(e)
        t=np.dot(P-A,e)/np.dot(e,e)
        dist=np.linalg.norm(P-(A+np.clip(t,0,1)*e))
        out.append((s,t,dist,(a,b)))
    # orientation: inside if all s same sign as polygon orientation
    orient=np.sign(sum(np.dot(np.cross(V[faces[fi][k]]-V[faces[fi][0]],V[faces[fi][k+1]]-V[faces[fi][0]]),n) for k in range(1,len(faces[fi])-1)))
    out=[(s*orient,t,dist,e) for s,t,dist,e in out]
    return out
def step(fi,Gp=G):
    inf=info(fi,Gp)
    if all(s>0 for s,_,_,_ in inf): return None
    # tip over the outside edge nearest to P whose foot is on the segment, else nearest outside edge
    outs=[x for x in inf if x[0]<0]
    cand=[x for x in outs if 0<=x[1]<=1] or outs
    s,t,dist,e=min(cand,key=lambda x:x[0])
    return adj(fi,e)
# distances: how far must G move (fraction of length) before another face becomes stable
def poly_dist(fi,Gp=G):
    inf=info(fi,Gp)
    if all(s>0 for s,_,_,_ in inf): return -min(s for s,_,_,_ in inf)
    return min(d for s,t,d,e in inf)

def roll_path(start,Gp=G):
    path=[start]; f=start
    while True:
        g=step(f,Gp)
        if g is None: return path
        if g in path: return path+[g]
        path.append(g); f=g
if __name__=='__main__':
    for start in range(14): print(start, roll_path(start))
    for fi in range(14): print(fi, '%.4f mm per 100 mm'%(poly_dist(fi)/L*100))